An extension based on qR-integral for a sequence of operators

The paper deals with a sequence of linear positive operators introduced via q-Calculus. We give a generalization in Kantorovich sense of its involving qR-integrals. Both for discrete operators and for integral operators we study the error of approximation for bounded functions and for functions having a polynomial growth. The main tools consist of the K-functional in Peetre sense and different moduli of smoothness.